Standardized precipitation index formula

[safina]

Can some help me what really is the formula of the standardized precipitation index and how will it be computed?

I am thinking of using the index to classify the 40 years into dry year, average year , or wet year using total annual rainfall data. I understand that SPI is an index based on the probability of recording a given amount of precipitation, and the probabilities are standardized so that an index of zero indicates the median precipitation amount.

Does the definition mean that we need first to calculated the probability of rainfall before it will be standardized (by (x value-mean)/ standard deviation)? If yes, how will the probabilities of rainfall be computed?

Please help.

 

[Valkarie]

The formula for the Standardized Precipitation Index (SPI) is as follows: SPI = (x - μ) / σ where x is the amount of precipitation recorded in a given period, μ is the mean precipitation over the same period, and σ is the standard deviation of the precipitation over the same period. In order to calculate the probabilities of rainfall, you will need to use the probability density function for the normal distribution. The probability density function can be used to determine the probability of observing a certain amount of precipitation in a given period. Once you have the probability of the observed precipitation, you can then calculate the SPI by subtracting the mean precipitation from the observed amount, and dividing it by the standard deviation of the precipitation.